What is the future of Arafat?

(CNN) --Israeli troops stormed Yasser Arafat's headquarters Thursday and blew up six buildings in the sprawling Ramallah, West Bank, compound in response to a Palestinian suicide attack on an Israeli bus that killed 17 passengers. The Israelis withdrew following the siege.

With events unfolding, "Crossfire" hosts Tucker Carlson and Paul Begala discussed the Middle East crisis with Hussein Ibish, communications director of the American-Arab Anti-Discrimination League, and Cliff May, president of the Foundation for the Defense of Democracies, focusing on the future of Arafat and the peace process.

BEGALA: Let me ask you about questions of strategy. Before Cliff was suggesting what the Israeli strategy might be. Clearly, the Palestinian strategy is to fund, encourage, reward and praise terrorism. That's clearly a fair strategy, isn't it?

IBISH: I don't think that's the strategy of the Palestinian Authority. ...

BEGALA: There's no doubt that it is.

IBISH: No, there is a big doubt that it is.

BEGALA: There's documented proof.

IBISH: I think there's a big doubt. This proof, so-called, was dismissed by the State Department so that it absolutely amounted to nothing. And you know that.

There is no doubt that there are extremists in the Palestinian movement, like Hamas and Islamic Jihad, who actually have in a way a common cause with the Israeli government -- extremists like [Israeli Prime Minister Ariel] Sharon -- in thwarting any peace process.

And each time there's a moment where Americans arrive, one or the other engages in some kind of gigantic escalation. And the reason is, both the Israeli government under Sharon, and the Palestinian extremist groups believe in a military solution. And Sharon says it outrightly. He says we can crush the Palestinians with brute force ...

BEGALA: Then why ...

IBISH: ... and force them to our will and make them live under our occupation and not be independent.

CARLSON: Let me -- you may be able to answer this question. And I've long wanted to hear the answer. Not defending Yasser Arafat, of course, but he is at the end of the day, a secular leader. And he's certainly, as Mr. Ibish I think implied, a better alternative than a lot of the alternatives we're aware of.

And I wonder if he is exiled or put on trial or executed or taken away from the scene in some way, who next? Who is this next generation of reasonable Palestinian leadership?

MAY: It's a very good question. We don't know the answer to that question. And the reason we don't know is because Arafat has very cleverly and assiduously made sure that there wouldn't be a next generation of moderate leaders who could succeed him.

In fact, one of the reasons they drag out into the street Palestinians who are accused of collaborating with Israel, who get no trial and are shot in the head and literally hang from posts, is that there shouldn't be anyone in that position.